Table 6.1 compares the expected SM yields and the yields observed in data for the mixed SR and for the most signal sensitive bins of the three-body shape-fit. From those, the p0 values are computed, confirming that no BSM physics was observed. While there is an excess of events in the mixed SR, all sensitive bins of the three-body shape-fit have at most as many events as expected. In the latter case, the p0 computation is skipped. The signal model independent upper limits are evaluated separately for the most signal-sensitive bins, one at a time.
1There is a remaining model dependence through the signal contamination in the CRs.
region / bin SM expected
data
obs. p0 nmaxnon´SM
exp. obs.
mixed SR 7.2˘ 1.0 10 0.13 7.0 9.7
threebody shape-fit:
amT2P r80,90sGeV,mTP r90,120sGeV 16.9˘ 2.8 12 ě0.5 9.9 7.3 amT2P r80,90sGeV,mTą120GeV 8.4˘ 2.2 8 ě0.5 7.8 7.9 amT2P r90,100sGeV, mTP r90,120s GeV 35˘ 4 29 ě0.5 14.7 11.7 amT2P r90,100sGeV, mTą120GeV 29˘ 5 22 ě0.5 47.8 55.4 Table 6.1: Expected and observed event yields for the mixed and three-body regions (most signal-sensitive bins), with systematic uncertainties for the expected yields. The p0 values indicate no significant deviation from the SM. The rightmost columns show the expected and observed upper limits placed on the number of non-SM events present in these regions, which can be used to constrain arbitrary models of BSM physics.
Figure 6.1 shows the observed exclusion probabilities computed with theCLsmethod for the mixed region, using a50%branching ratio for each decay mode (t˜1 Ñt`χ˜01 and
˜t1 Ñ b`χ˜˘1). The corresponding contour of the region excluded at 95% is shown in figure 6.2, also for branching ratios of25% and75%. The central part of the mass plane is expected to be excluded, although the observed reach is smaller than expected due to the slight observed excess.
Table 6.2 shows a summary of the additional 13 SRs defined in the full analysis [121].
ThetNregions have been optimised fort˜1 Ñt`χ˜01decays, targeting different parts of the m˜t1–mχ˜0
1 mass-plane: tN_diag for the region near the “diagonal” (kinematic boundary);
tN_med and tN_high for medium and high stop masses, respectively; and tN_boost for the highest stop masses and boosted topologies, where individual jets cannot always be fully resolved and may instead merge into one larger jet (reconstructed with the anti-kt algorithm with a size parameter ofR“1.0). ThebCregions have been optimised for the selection of t˜1 Ñ b`χ˜˘1 decays, assuming various mass differences between ˜t1,χ˜˘1, and
˜
χ01. Due to the additional sparticle in these decays, the parameter space to be covered is larger, and more regions have been defined. For the mixed models with mχ˜˘
1 “2ˆmχ˜0
1, mostly thebCcandbCdregions with are of interest, as thebCaandbCbregions primarily target compressed spectra with small mass differences.
The exclusion reach is augmented towards lower stop masses and towards the kine-matic boundary when these SRs are also taken into consideration. This is done by evaluating the performance of each SR at each mass point, always choosing the one with the lowest expected CLs value. The resulting exclusion reach is shown in figure 6.3, for several ˜t1 Ñt`χ˜01 branching ratios from 0% (t˜1 Ñ b`χ˜˘1 only) to100% (˜t1 Ñ t`χ˜01 only). For neutralino masses up to„160GeV, stop masses from the kinematic boundary up to about500GeV are excluded independently of the assumed branching ratio.
0.947 0.522 0.067 0.021 0.011 0.031 0.062 0.167 0.327 0.500 0.681 0.783 0.747 0.187 0.012 0.002 0.004 0.016 0.033 0.151 0.340 0.489 0.652 0.643 0.130 0.005 0.005 0.009 0.041 0.153 0.255 0.460 0.627 0.313 0.045 0.019 0.040 0.127 0.271 0.400 0.581 0.336 0.145 0.134 0.261 0.424 0.580 0.483 0.416 0.416 0.577 0.686 0.659
200 300 400 500 600 700 800
0 100 200 300 400 500 600
[GeV]
t~1
m [GeV] 10χ∼m
a) ExpectedCLs values
0.950 0.677 0.200 0.087 0.053 0.116 0.192 0.376 0.569 0.667 0.758 0.821 0.798 0.398 0.056 0.011 0.022 0.073 0.123 0.351 0.582 0.662 0.742 0.737 0.316 0.028 0.027 0.045 0.145 0.356 0.491 0.649 0.728 0.552 0.151 0.082 0.141 0.316 0.509 0.625 0.705 0.578 0.342 0.325 0.498 0.634 0.704 0.659 0.631 0.631 0.703 0.761 0.746
[GeV]
t~1
m
200 300 400 500 600 700 800
[GeV] 1 0χ∼m
0 100 200 300 400 500 600
b)Observed CLs values
Figure 6.1: a) Expected and b) observed CLs values for the mixed region, using stop pair production models with50% branching ratio for either˜t1 Ñt`χ˜01 ort˜1 Ñb`χ˜˘1. The chargino mass is chosen asmpχ˜˘1q “2ˆmpχ˜01q, and all charginos decay intoW`χ˜01.
Figure 6.2: Mixed stop pair-production models excluded by the mixed SR developed in this thesis. The exclusion contour is shown for different branching ratios of ˜t1 Ñt`χ˜01 and˜t1Ñb`χ˜˘1 decays. In each case, the observed (expected) exclusion contour is shown as a solid (dashed) line. Since no other stop decay modes are considered in the models, the two branching ratios always sum up to 1. At a ˜t1 Ñt`χ˜01 branching ratio of 25%, no signal models were observed to be excluded, and only the expected exclusion contour is shown.
region Signal scenario Exclusion technique
tN_diag ˜t1Ñt`χ˜01,m˜t1Ámt`mχ˜01 shape-fit (ETmissandmT) tN_med ˜t1Ñt`χ˜01,m˜t1„550 GeV,mχ˜01À225GeV cut-and-count
tN_high ˜t1Ñt`χ˜01,m˜t1Á600 GeV cut-and-count tN_boost ˜t1Ñt`χ˜01,m˜t1Á600 GeV, with aR“1.0 jet cut-and-count bCa_low ˜t1Ñb`χ˜˘1,∆M À50GeV shape-fit (leptonpT)
˜t1Ñbf f1χ˜01
bCa_med ˜t1Ñb`χ˜˘1,50GeVÀ∆M À80GeV shape-fit (leptonpT)
˜t1Ñbf f1χ˜01
bCb_med1 ˜t1Ñb`χ˜˘1,∆mÀ25GeV,m˜t1À500 GeV shape-fit (amT2) bCb_high ˜t1Ñb`χ˜˘1,∆mÀ25GeV,m˜t1Á500 GeV shape-fit (amT2)
bCb_med2 ˜t1Ñb`χ˜˘1,∆mÀ80GeV,m˜t1À500 GeV shape-fit (amT2 andmT) bCc_diag ˜t1Ñb`χ˜˘1,mt˜1 Ámχ˜˘
1 cut-and-count
bCd_bulk ˜t1Ñb`χ˜˘1,∆M,∆mÁ100 GeV,m˜t1À500GeV shape-fit (amT2 andmT) bCd_high1 ˜t1Ñb`χ˜˘1,∆M,∆mÁ100 GeV,m˜t1Á500GeV cut-and-count
bCd_high2 ˜t1Ñb`χ˜˘1,∆M Á250GeV, m˜t1 Á500GeV cut-and-count
Table 6.2: Summary of additional SRs in the published analysis [121], the targeted signal scenarios, and the analysis technique used for model-dependent exclusions For the
˜t1 Ñ b`χ˜˘1 decay scenarios, the mass splittings ∆M “ mpt˜1q ´mpχ˜01q and ∆m “ mpχ˜˘1q ´ mpχ˜01q are used to characterise the mass hierarchies. The regions tN_med, tN_high,tN_boost,bCc_diag,bCd_high1, andbCd_high2use a CR-based normalisation as is done for the mixed SR. This technique is referred to as cut-and-count, while the remaining regions use a shape-fit technique with bins defined in one or two variables, similar to the three-body region.
[GeV]
t1
m~
300 400 500 600 700
[GeV] 10m
Expected limits Observed limits All limits at 95% CL
T
Figure 6.3: Excluded stop pair-production models using the SR from the full stop 1-lepton analysis with the lowest expected CLs at each point.
The expected and observed CLs values for the three-body region are shown in fig-ure 6.4. Here, no combination with other regions is needed. Figfig-ure 6.5 shows the resulting exclusion contour, along with the exclusion contours for on-shellt˜1 Ñt`χ˜01 decays and four-body stop decays (˜t1 Ñ b```´χ˜01 or bqq¯χ˜01) from the published analysis. For inter-mediate ∆m, stop masses up to300GeV are excluded using the three-body shape-fit.
We conclude this section by revisiting the topic of systematic uncertainties. Up to this point, they were accounted for as uncertainties on the expected yields, and the likelihood fit made small adjustments to their magnitude in order to find the overall best description of the observed data. At the end of the day, however, we’re interested in the estimated signal strengthµsig, or theCLsfor a given signal model. Table 6.3 shows how these statistical measures change if only a limited number of systematic uncertainties are accounted for in the fit model. Removing degrees of freedom from a fit can lead to problems in the convergence; in some cases this effect was mitigated by constraining the normalisation coefficientsµt¯tandµW to the confidence interval found in the background-only fit. The change to the best-fit value of µsig is typically small compared to the change of its uncertainty∆µsig. As long as this is the case, studying the change of∆µsig is equivalent to studying the effect on CLs. Table 6.4 shows this decomposition of the signal strength uncertainty for three additional benchmark points.
Large contributions stem from the jet energy scale and resolution uncertainties, for the non-excluded models, the sensitivity tob-tagging andt¯tmodelling uncertainties becomes
0.01 0.01 0.110.09
100 150 200 250 300 350 400 450 0
a) ExpectedCLs values
0.00 0.00 0.050.07
100 150 200 250 300 350 400 450 0
b)Observed CLs values
Figure 6.4: a) Expected and b) observed CLs values for the three-body region, using stop pair production models with off-shell top quarks (mW ă∆m“m˜t1´mχ˜0
1 ămt).
[GeV]
t1
m~
200 300 400 500 600 700 800
[GeV] 10m
All limits at 95% CL
T
Figure 6.5: Excluded stop pair-production models, assuming 100% ˜t1 Ñ t`χ˜01 decays.
From left to right, the different areas correspond to four-body, three-body and two-body decays. The shown three-body stop exclusion is obtained using only the three-body shape-fit presented in this thesis; the other stop decay modes are excluded by other SRs from the full stop 1-lepton analysis. The expected exclusion contour is shown in black, with the experimental˘1σ uncertainty band in yellow; the observed contour is shown in red, with the ˘1σ theory uncertainty as dashed lines.
larger. While the observedCLsvalues for the non-excluded mixed and three-body models are similar, the uncertainties on the signal strength is very different; this is related to the data excess in the mixed SR, which results in a non-zero best-fit result forµsig, making it more difficult to exclude the mixed scenario even when the uncertainty onµsigis smaller.
As the expected signal contamination in the CRs is low, the fit parameters found in the background-only fit will also describe the signal+background CR yields well; the fit will accommodate any excess in the SR by increasing theµsigparameter. This does not allow any conclusion on the nature of the observed excess –it may be due to a SUSY signal, but could equally well be an underestimated SM process, or merely a statistical fluctuation–
but it will be worthwhile to check whether a similar excess can be observed also in the larger data sample to be recorded during LHC run 2.
omitted uncertainty µsig change CLs
none 0.2345˘0.2645 0.0268
JER 0.2306˘0.2390 0.1133 0.0208
JES 0.2352˘0.2417 0.1074 0.0213
b-tagging 0.2320˘0.2435 0.1033 0.0249 other SM backgrounds 0.2318˘0.2435 0.1032 0.0256 t¯tmodel 0.2306˘0.2445 0.1008 0.0260 ETmiss soft-term 0.2311˘0.2455 0.0983 0.0261 W+jets model 0.2313˘0.2455 0.0983 0.0262 pile-up model 0.2312˘0.2456 0.0982 0.0262
Table 6.3: Effect of different systematic uncertainties on µsig and CLs for the mixed SR using an excluded signal model (˜t1 500 GeV, χ˜˘1 300 GeV, χ˜01 150 GeV, 50% BR), using the event yields observed in data. The result obtained by the complete fit model is shown in the first line. The contributions of systematic uncertainties are estimated by removing fit parameters related to one source of systematic uncertainty at a time. The shifts of the central value forµsig is small compared to the change of the corresponding uncertainty∆µsig. The quoted change to∆µsig is the squared difference with respect to the complete fit; due to correlations, the individual contributions to do not add up to the full uncertainty.
region / model mixed SR three-body SR mp˜t1q, mpχ˜01q (GeV) 500,150 600,200 200,50 300,180
JES 0.1074 0.1550 0.2016 0.2745
JER 0.1133 0.0577 0.0357 0.4183
b-tagging 0.0983 0.1857 0.1271 0.4273 ETmiss soft-term 0.0982 0.1060 0.0462 0.2181
pile-up model 0.1033 0.0262 0.0486 0.0647
tt¯model 0.1008 0.1519 0.1086 0.2553
W+jets model 0.0983 0.0251 0.0513 0.2275
other SM backgrounds 0.1032 0.0361 0.0276 0.2026 total uncertainty 0.2645 0.4343 0.1410 0.6732 observedCLs 0.0268 0.1407 6.7ˆ10´5 0.1769
Table 6.4: Contribution of different systematic uncertainties to the uncertainty on the signal strength, ∆µsig, determined with the same method as used for table 6.3. The re-sults from table 6.3 are repeated for comparison with a non-excluded benchmark point for the mixed signal regions, as well as two benchmark points (excluded and non-excluded) for the three-body signal region.